GZK cutoff distortion due to the energy error distribution shape

The observed energy spectrum of ultra high energy cosmic rays (UHECR) is distorted by errors in the energy reconstruction. Here we show that if the shape of the error distribution is lognormal, the high end of the cosmic ray spectrum will be distorted. This is distinct and potentially more significant than the effect of the magnitude of the error in the energy. We estimate the UHECR spectrum at the Earth assuming it is originated from a cosmological flux. We then convolute this flux assuming a lognormal error in the energy. We show that if the standard deviation of the lognormal error distribution is equal or larger than 0.25, both the shape and the normalization of the measured energy spectra will be modified significantly. As a consequence the GZK cutoff might be sufficiently smeared and as not to be seen. This result is independent of the power law of the cosmological flux. As a conclusion we show that in order to establish the presence or not of the GZK feature, not only more data is needed but also that the shape of the energy error distribution has to be known well.